Total Absorption in Finite Time in an $iδ$ Potential

Details Total Absorption in Finite Time in an $iδ$ Potential Total Absorption in Finite Time in an $iδ$ Potential

2001-07-30

arxiv.org/abs/quant-ph/0107152v1

Physics

Quantum Physics

8 pages, no figures, we would welcome comments

Scientific paper

We consider the evolution of Green's function of the one-dimensional Schr\"odinger equation in the presence of the complex potential $-ik\delta(x)$. Our result is the construction of an explicit time-dependent solution which we use to calculate the time-dependent survival probability of a quantum particle. The survival probability decays to zero in finite time, which means that the complex delta potential well is a total absorber for quantum particles. This potential can be interpreted as a killing measure with infinite killing rate concentrated at the origin.

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